Question

The period T of a simple pendulum is expressed by: √ where ‘l' is the length of the pendulum and ‘g' is the acceleration due to gravity. Show that the formula is dimensionally consistent

Answer 1

T = T

Step-by-step explanation:

The period of a simple pendulum is given by the formula

`t = 2\pi \sqrt{(l)/(g) }`

Where

l - length of the pendulum

g - acceleration due to gravity

The dimension of the physical quantities are given by,

t - T

l - L

g - m/s² - LT⁻²

Substituting in the above equation,

T = 2π √(L / LT⁻²)

Considering only the dimensional units in the equation

T = √(L / LT⁻²)

T = T

This shows that the formula for a simple pendulum is dimensionally consistent, T = T